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Cambridge
TECHNICALS
CAMBRIDGE TECHNICALS
IN ENGINEERING
LEVEL 3 UNIT 1 – MATHEMATICS FOR
ENGINEERING
DELIVERY GUIDE
Version 1
OCR
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VEL CONTENTS
3
CA
MBRIDGE
TECHNICALS
IN
ENGINEERING
Introduction 3
Key Terms 4
Misconceptions 7
Suggested Activities:
Learning Outcome (LO1) 8
Learning Outcome (LO2) 10
Learning Outcome (LO3) 11
Learning Outcome (LO4) 12
Learning Outcome (LO5) 14
Learning Outcome (LO6) 15
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A
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TICS
FOR
ENGINEERING
2
INTRODUCTION
ENGINEERING
This Delivery Guide has been developed to provide practitioners with a variety of Foreword: Resources FOR
creative and practical ideas to support the delivery of this qualification. The Guide There are a wide range of resources that may be useful in supporting the delivery of this TICS
is a collection of lesson ideas with associated activities, which you may find helpful unit, some of which have been listed in the separate Resources Link resource available A
as you plan your lessons. from http://www.ocr.org.uk/qualifications/cambridge-technicals-engineering-level-3/. THEM
These include reference text books, web-based tutorials, web-based video tutorials and A
OCR has collaborated with current practitioners to ensure that the ideas put forward in worked and practice questions. M
this Delivery Guide are practical, realistic and dynamic. The Guide is structured by learning
outcome so you can see how each activity helps you cover the requirements of this unit. Many resources will singularly cover the entire content of this unit, and for this reason
We appreciate that practitioners are knowledgeable in relation to what works for them specific resources have not been listed against each topic area. Although there are
and their learners. Therefore, the resources we have produced should not restrict or many resources that cover mathematical concepts generically, some are dedicated to
impact on practitioners’ creativity to deliver excellent learning opportunities. the application of mathematics in the context of engineering. Teachers and learners are
encouraged to solve problems related to engineering where possible.
Whether you are an experienced practitioner or new to the sector, we hope you find The following two books (which also include further web-based resources and which
something in this guide which will help you to deliver excellent learning opportunities. are available as paperback or e-book) are highly recommended:
If you have any feedback on this Delivery Guide or suggestions for other resources you Bird, John (2014) ‘Basic Engineering Mathematics’ – Routledge, UK
would like OCR to develop, please email resources.feedback@ocr.org.uk. Bird, John (2014) ‘Engineering Mathematics’ – Routledge, UK
Unit aim Unit 1 Mathematics for engineering
LO1 Understand the application of algebra relevant to engineering problems
Mathematics is one of the fundamental tools of the engineer. It underpins every branch of LO2 Be able to use geometry and graphs in the context of engineering
engineering and the calculations involved are needed to apply almost every engineering problems
skill. LO3 Understand exponentials and logarithms related to engineering problems
This unit will develop learners’ knowledge and understanding of the mathematical
techniques commonly used to solve a range of engineering problems. LO4 Be able to use trigonometry in the context of engineering problems
By completing this unit learners will develop an understanding of: LO5 Understand calculus relevant to engineering problems
• algebra relevant to engineering problems Be able to apply statistics and probability in the context of engineering
• the use of geometry and graphs in the context of engineering problems LO6 problems
• exponentials and logarithms related to engineering problems
• the use of trigonometry in the context of engineering problems ENGINEERING
• calculus relevant to engineering problems Opportunities for Maths skills development IN
• how statistics and probability are applied in the context of engineering problems
This unit provides a range of activities entirely focussed on Mathematics for Engineering.
Please note TECHNICALS
The activities are not designed to replace you own subject knowledge and expertise in
The timings for the suggested activities in this Delivery Guide DO NOT relate to the Guided deciding what is most appropriate for your learners.
Learning Hours (GLHs) for each unit.
Assessment guidance can be found within the Unit document available from MBRIDGE
Maths CA
www.ocr.org.uk. 3
The latest version of this Delivery Guide can be downloaded from the OCR website. VEL
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KEY TERMS
UNIT 1 – MATHEMATICS FOR ENGINEERING ENGINEERING
FOR
TICS
Explanations of the key terms used within this unit, in the context of this unit A
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Key term Explanation A
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Algebra Algebra is an area of mathematics in which letters and other general symbols are used to represent numbers and quantities in formulae and equations.
Angles and radians Converting from angle to radians: 360˚= 2 π radians i.e. x radians = 180°x/π degrees;
Arcs x degrees = πx/180° radians
Arc length s = rθ where θ is in radians 2
Binomial expression A binomial is a mathematical expression (a polynomial) with two terms eg 3x +2 or 5x -1
Circles - areas 2
The area of a circle: area = πr 2 2 2
Circles – co-ordinate The co-ordinate equation of a circle: (x – a) + (y – b) = r
equation
Co-ordinate Co-ordinate geometry, or Cartesian geometry, is the study of geometry using a coordinate system.
geometry
Curve sketching Curve sketching is the sketching of mathematical functions in order to visualise their shape and is often used to determine solution(s).
Definite integrals A definite integral is an integral expressed as the difference between the values of the integral at specified upper and lower limits of the independent variable.
Differentiation – ax
exponentials and Differentiation of expressions containing e and ln ax
logarithms n
Differentiation – The derivative is the instantaneous rate of change of a function with respect to one of its variables. Simple functions are taken to contain terms of the formy = ax ENGINEERING
simple functions IN
Differentiation Differentiation of expressions containing the terms sine (sin) and cosine (cos).
– trigonometric
function TECHNICALS
Exponential An exponential function is a function whose value is a constant raised to the power of the argument. In this unit, it is taken to be of the form y = ex and y = e-x
function MBRIDGE
Factorisation Factorisation is the reverse of expanding brackets. For example putting 2x² + x - 3 into the form (2x + 3)(x - 1) CA
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